Emergent Formalization (Language)

Prime #

312

Origin domain

Linguistics & Semiotics

Also from

Systems Thinking & Cybernetics, Tech Ethics Ai Governance

Aliases

Grammaticalization, Institutionalization of Practice, Codification of Convention

Related primes

Emergence, Path Dependence, Compositionality

Core Idea

Emergent Formalization is the historical-linguistic process by which informal usage patterns crystallize into formal grammatical structures over centuries of language change. Distinct from synchronic formalization in logic and formal systems, emergent formalization names the diachronic trajectory: (1) an informal usage pattern arises through frequency-based regularity in speech communities, (2) the conventionalization process selects stable forms via Bybee's chunking mechanisms and token-frequency effects (Bybee 2003, 2010), (3) the grammaticalization trajectory traces the unidirectional semantic bleaching documented by Hopper and Traugott (1993/2003), and (4) the formal-grammar emergence marks the point at which usage patterns acquire rule status in the grammar. The mechanism is distinctly linguistic: frequency-driven token consolidation → phonetic reduction → loss of compositional transparency → reanalysis as a morphosyntactic unit (Bybee & Perkins 1994; Heine & Kuteva 2002).^[1]

How would you explain it like I'm…

How Words Become Rules

When lots of people say the same little phrase over and over, like 'gonna' instead of 'going to,' it slowly becomes a real way to talk. Nobody made a rule. The habit just got squished together so much that it turned into one new word.

Habits Turn Into Grammar

Languages change slowly over hundreds of years. Sometimes people start using a phrase in a casual way, and they say it so often that it gets shorter and sticks together. Eventually it becomes a real grammar rule that everyone follows without thinking. For example, 'I am going to eat' became 'I'm gonna eat.' The new piece behaves like a single word now, not the old phrase it came from. That slow process — informal habit hardens into a real grammar rule — is emergent formalization.

Usage Patterns Hardening Into Grammar

Emergent formalization is how informal speech patterns slowly turn into formal grammar over generations. It happens in roughly four stages. First, an informal usage pattern shows up because speakers repeat a phrase a lot. Second, frequent use locks the form in through what linguists call chunking. Third, the chunk goes through grammaticalization: meaning bleaches, the form shortens, and it loses its original transparency. Finally, the result has rule-like status in the grammar, used automatically by new speakers. This is different from formalization in logic or math, where a designer writes rules on purpose. In language it just happens — frequency and use do the work without any planner.

 

Emergent formalization is the diachronic linguistic process by which informal usage patterns crystallize into formal grammatical structures over long stretches of historical time. Distinct from synchronic formalization in logic or formal systems, where rules are explicitly stipulated by a designer, emergent formalization is a bottom-up trajectory driven by usage frequency. The mechanism unfolds in stages: (1) an informal pattern arises through frequency-based regularity in a speech community, (2) the pattern conventionalizes via *chunking* — adjacent elements consolidated into a single cognitive unit (Bybee 2003, 2010), (3) grammaticalization proceeds through semantic bleaching, phonetic reduction, and loss of compositional transparency (Hopper and Traugott 1993/2003), and (4) the consolidated chunk acquires rule status in the grammar, governing new utterances. Classic trajectories include the English future-marker shift from 'be going to' (motion verb) to 'gonna' (auxiliary), and Heine and Kuteva's (2002) cross-linguistic catalog of recurrent grammaticalization paths. The pattern documents how grammar can emerge without any explicit rule-maker.

Structural Signature

The signature rests on six italicized role-phrases capturing the internal mechanics:^[2]

• The informal usage pattern — initial high-frequency collocations or semi-productive constructions (e.g., motion verb + locative "I go to X" repeated thousands of times);
• The conventionalization process — token-frequency effects select phonologically reduced allomorphs, blocking reanalysis; chunking reduces internal transparency (Bybee 2010);
• The grammaticalization trajectory — unidirectional semantic bleaching follows Hopper-Traugott's cline: lexical → semi-functional → fully grammatical (Hopper 1991; Hopper-Traugott 2003);
• The formal-grammar emergence — the category acquires rule status, obligatory inflectional marking, or morphosyntactic constraints absent in the source construction;
• The frequency-effect mechanism — token frequency in utterances, not type frequency, drives the phonetic reduction and constituency loss characteristic of grammaticalization (Bybee & Perkins 1994);
• The unidirectional cline — movement is monotonic: lexical items become grammatical but not vice versa without external intervention (Traugott 1989; challenged by Haspelmath 2004).

The process is one-way in practice (grammaticalizations rarely revert without rupture), produces an audit trail (Old English documents preserve full willan, Modern English reduces to will), and is driven by the interaction of (a) frequency-based phonetic erosion, (b) reanalysis of categorical boundaries, and © community-wide adoption thresholds. The mechanism differs sharply from ad-hoc formalization in organizations (standards bodies) or technology (API codification) — this one is unconscious, collective, and played out over centuries, not years or decades.^[3]

What It Is Not

• Not synchronic formalization — which constructs formal systems (logic, mathematics) deliberately; emergent formalization is diachronic and implicit.
• Not all language change — only the subset involving morphosyntactic structure emergence from free-form usage.
• Not just grammaticalization — grammaticalization is the kernel case, but emergent formalization is the broader epistemic category: grammaticalization is emergent formalization in the linguistic domain.
• Not deductive formalization — which applies rules top-down; emergent formalization recognizes and codifies patterns already in use.
• Not lexicalization alone — which produces new words; grammaticalization produces new morphemes and function words, a distinct trajectory.
• Not pure conventionalization — conventionalization can stabilize ad-hoc forms without formal rule-status (e.g., a shared slang term); grammaticalization necessarily produces rule-governed morphosyntactic units.^[4]

Grammaticalization Mechanisms and Cognitive Grounding

The cognitive substrate of emergent formalization rests on usage-based grammar theory (Bybee 2010; Langacker 1987). Speakers chunk high-frequency sequences into single phonological units; this chunking reduces internal transparency, allowing reanalysis of categorical boundaries. For example, going to appears in millions of utterances with future-time semantics ("I am going to leave"); the sequence becomes automatized; phonetic reduction (gonna) follows naturally; the original motion-verb semantics bleaches away; speakers reanalyze the entire chunk as a single future-marking unit rather than a biclausal construction. This reanalysis is not conscious rule-learning but emerges from the implicit patterns children extract from the input they hear. The frequency threshold is empirically predictable: Bybee's data show that constructions crossing 1,000 token-frequency in a corpus typically begin showing grammaticalization morphology (reduction, fusion, loss of independent stress).^[1]

The unidirectional cline (Hopper-Traugott) tracks semantics: lexical verbs (concrete, agentive) → auxiliaries (aspectual, tense) → inflectional affixes (purely formal), with semantic bleaching at each step. Functional morphology (plural -s, past -ed) shows vestiges of source constructions (plurals from reflexive/emphatic uses; past tense from perfect-aspect auxiliaries like have). The cline is supported cross-linguistically (Heine-Kuteva 2002 document ~300 pathways), but Haspelmath (2004) challenges strict unidirectionality, citing counterexamples (de-grammaticalization, lateral movement).^[5] The tension remains live in the field.^[6]

Broad Use: Linguistics, Language Change, and Computational Modeling

Emergent formalization is foundational to four interlocking domains:

1. Historical-comparative linguistics: The Hopper-Traugott framework explains Indo-European conjugational systems, Sino-Tibetan classifiers, Bantu noun-class systems — all historically traceable to content words (body-part nouns, classification verbs). Traugott and Dasher (2002) show how the same semantic pathways repeat across unrelated languages.^[7]

2. Language acquisition studies: Children acquiring a language do not receive explicit rules; they extract regularities from utterances. Grammaticalization research illuminates how implicit frequency-based learning yields adult-like morphosyntactic competence. Bybee (2003) argues that high-frequency tokens in child speech show phonetic reduction and reanalysis patterns identical to historical grammaticalization.^[8]

3. Computational linguistics: Models of language change (Croft 2000; Kroch 1989) must account for how rare, high-frequency-biased innovations propagate through populations. Agent-based simulations (Schoenemann et al., Tamariz & Kirby) attempt to model the emergence of grammatical structure from usage patterns without pre-specified rules. The challenge: frequency-driven chunking and reanalysis are hard to implement in standard symbolic parsers.

4. Cognitive linguistics: Usage-based frameworks (Langacker, Bybee) treat grammatical structure as emergent from exemplars stored in memory. Grammaticalization is the mechanism by which exemplar distributions, shaped by frequency and phonetic reduction, produce new categorical divisions and rules.

The theory also bridges to non-linguistic domains: organization theory (Suchman 1987; Pentland & Feldman 2005) studies how ad-hoc workarounds become inscribed in standard operating procedures; standards bodies (IETF, W3C) explicitly privilege observed practice over a priori design. But the linguistic case is the archetype: grammaticalization is emergence without design, without intention, playing out over centuries.^[9]

Examples

Formal Example: English going to → gonna

Mapped back: The motion-verb construction go to X (locative, fully compositional) appears in Middle English with future-oriented semantics ("I go to the wars" = "I am going to the wars"). By Early Modern English, this construction dominates future-reference contexts. The sequence going to undergoes chunking in high-frequency tokens; phonetic reduction follows (go-na, gon-na, gonna); the original motion and destination semantics bleach away — gonna no longer implies actual movement or a specific location. By 18^th-century English, gonna is no longer analyzable as go+to; it is a future-marking grammatical element. The Hopper-Traugott cline is textbook: lexical verb (motion, agentive) → semi-functional auxiliary (tense/aspect marking) → near-fully-grammatical future marker (Hopper-Traugott 2003; Bybee 2010 corpus analysis shows the phonetic reduction timeline explicitly).^[2]

Applied Example: Emoji Unicode Standardization

Mapped back: Informal Internet usage of text-based emoticons and later emojis in the 1990s–2000s shows the emergent-formalization signature in a contemporary setting. Users improvised emoji sequences (😂, 🤔) with locally-variable semantics and high register-specific variation. High-frequency usage in chat and messaging created implicit standardization pressures; carrier systems (iOS, Android, SMS) selected for canonical forms. By 2010, the Unicode Consortium formally recognized emoji as graphemic units, assigning code points and official semantics to each. The formal registry crystallized the informal innovation. Modern AI-generated emoji proposals reflect ongoing pressure for further emergent formalization — new usage patterns (e.g., toned skin-color modifiers, gender-neutral figures) are informally used, then face formalization cycles as they enter Unicode standards. The mechanism parallels grammaticalization: high-frequency informal usage → community recognition → formal codification → loss of original context-sensitivity.^[7]

Both examples show the signature: (1) ad-hoc, high-frequency usage patterns, (2) phonetic/graphemic reduction and automatization, (3) reanalysis (no longer decomposable into component meanings), (4) formal rule-status assignment, (5) semantic bleaching (original meaning is inaccessible or irrelevant).

Structural Tensions and Open Questions

T1 — Unidirectionality hypothesis vs. counterexamples. Traugott and Hopper argue for strict unidirectionality: lexical → grammatical, never reversed. Haspelmath (2004) and Newmeyer (2001) document cases of de-grammaticalization (affixes becoming word-like again, auxiliaries losing functional status in certain contexts). The field splits: universalists defend unidirectionality with principled exceptions (affixes absorbed by analogy); relativists argue the cline is directional only probabilistically, not absolutely. Cross-linguistic data (Heine-Kuteva lexicon; Lehmann 2015) support strong unidirectionality in most cases but invite caution on universal claims.

T2 — Grammaticalization vs. lexicalization. Both produce formal categories, but lexicalization (e.g., metaphor → fixed idiom: "raining cats and dogs") does not reliably generate morphosyntactic structure or obligatory marking. Kuteva (2001) argues lexicalization is a parallel but distinct process; Bybee treats all category-formation as emergent from usage.^[10] The boundary between grammaticalization (structure-building) and lexicalization (inventory-building) remains blurry in practice.

T3 — Cognitive vs. functional motivation. Is grammaticalization driven by ease of processing (chunking, reduction) or communicative utility (future marking is useful; modal auxiliaries are useful)? Bybee emphasizes frequency and automatization (cognitive); Hopper stresses functional need and semantic specialization (functional). Evidence supports both: frequency-driven phonetic reduction is mechanistic; the selection of which high-frequency patterns survive to grammaticalization may be utility-driven.^[11]

T4 — Cross-linguistic universals vs. variation. Do all languages grammaticalize motion verbs as future markers? Heine-Kuteva data suggest pathways are remarkably constrained (motion → future; possessive → existence/past; come → comitative). Yet variation persists: English grammaticalized will as future, but Spanish did not grammaticalize ir (Spanish uses periphrastic ir a for immediate future, distinct from synthetic future -ré). The balance between universal cognitive pressures and language-specific historical accidents remains an open question.^[12]

Structural–Framed Character

Emergent Formalization is a hybrid on the structural–framed spectrum, and the frame here is substantial even though a structural core exists. Part of it is a bare pattern — frequent informal usage gradually hardening into stable, rule-governed structure; part of it is a vocabulary and set of assumptions inherited from historical linguistics.

The structural kernel is a general trajectory: high-frequency, loosely-organized behavior is selected and conventionalized over time until it crystallizes into a fixed form. But the prime does not travel as a bare crystallization process. It imports the concepts and machinery of diachronic linguistics — speech communities, Bybee's frequency-driven chunking, grammaticalization, the move from collocation to grammatical structure — and it presupposes the specific subject matter of language change. Its home cases are linguistic: a motion-verb phrase becoming a future-tense marker, an informal turn becoming standard grammar over centuries. Because making sense of the idea requires importing the lens and vocabulary of how languages formalize their own usage, rather than simply spotting a pattern in any system, it sits on the framed side of the middle even though a general crystallization shape lies underneath.

Substrate Independence

Emergent Formalization (Language) is a moderately substrate-independent prime — composite 3 / 5 on the substrate-independence scale. The process — informal usage conventionalizing into formal structure through frequency-driven crystallization — is structurally suggestive and could in principle describe cultural evolution or the hardening of institutional norms. But it is grounded in linguistics and language change, and the proposed extensions to other domains read as metaphorical rather than structural reuse. So while the underlying logic hints at wider applicability, in practice the prime stays a language-change phenomenon, which holds it to the middle of the scale.

• Composite substrate independence — 3 / 5
• Domain breadth — 3 / 5
• Structural abstraction — 4 / 5
• Transfer evidence — 2 / 5

Relationships to Other Abstractions

Current abstraction Emergent Formalization (Language) Prime

Parents (1) — more general patterns this builds on

• Emergent Formalization (Language) is a decomposition of Emergence Prime

  Emergent formalization is the specific shape emergence takes when informal usage patterns crystallize into formal grammatical structure over time.

Hierarchy path (1) — routes to 1 parentless root

• Emergent Formalization (Language) → Emergence → Micro Macro Linkage

Neighborhood in Abstraction Space

Emergent Formalization (Language) sits in a sparse region of abstraction space (69^th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely rather than landing on a neighbor.

Family — Unclustered & Miscellaneous (429 primes)

Nearest neighbors

• Semantic Shift — 0.72
• Speech Act Theory (Illocution, Perlocution) — 0.71
• Semantic Narrowing and Widening — 0.70
• Linguistic Universals — 0.69
• Iconicity — 0.69

Computed from structural-signature embeddings · 2026-07-26

Not to Be Confused With

Emergent Formalization must be distinguished from Formalization itself, though the two are closely related. Formalization is the process of taking informal, tacit, or intuitive knowledge and expressing it in explicit, structured, often mathematical form—a set of axioms, definitions, rules, or algorithms that capture the essential logic of the domain. Emergent Formalization specifically describes formalization that arises not by initial deliberate design but through iterative discovery and synthesis from concrete practice, patterns, examples, and tacit understanding that practitioners accumulate. Formalization is the act and outcome of expressing knowledge explicitly; Emergent Formalization names the temporal and epistemic process by which formal systems gradually crystallize from informal grounding. Both involve the creation of explicit structure, but formalization can be top-down (designing axioms and rules from first principles and then applying them to practice) or bottom-up (observing practice, extracting patterns, gradually articulating rules). Emergent Formalization emphasizes the bottom-up, discovery-based aspect. The distinction matters because it clarifies why some formal systems (mathematics developed from axioms) feel elegant but disconnected from practice, while others (statistics developed from practical problems of insurance and agriculture) feel grounded and transferable. Both pathways are valuable, but they produce different epistemological stances and practical consequences.

Emergent Formalization is also distinct from Abstraction, though the two often occur together. Abstraction is the process of selectively filtering and retaining essential features while discarding inessential detail—a circuit diagram abstracts away the physical substrate of electronics and retains only functional relationships. Abstraction is about reduction and compression. Emergent Formalization is about explication and structure-building—taking implicit, intuitive understanding and making it explicit, formal, and rigorous. Abstraction often precedes formalization (you abstract to identify the essential features you want to formalize), but they are not the same operation. An artist might abstract visual patterns in nature into essential shapes; a mathematician might then formalize those abstractions into geometric structures. Abstraction prepares the conceptual ground; formalization builds explicit structure. You can have pure abstraction without formalization (a poet abstracting emotion into metaphor without mathematical structure), and you can have formalization without prior abstraction (writing down rules for a process you already understand implicitly, without abstracting away inessential details). The two concepts are most powerful in combination but remain distinct.

Emergent Formalization differs from Canonicalization, though the two can coincide. Canonicalization is the process of establishing a standard, reference, or official version of something—a canonical text, a canonical form of an equation. Canonicalization is about standardization and reference-setting. Emergent Formalization is about the process and structure of making tacit knowledge explicit. A formal mathematical framework might emerge from practice, and then be canonicalized (enshrined in textbooks, made official, adopted by a field). Canonicalization follows and institutionalizes formalization; it is not formalization itself. The two often co-occur—a field that formalizes its knowledge through emergent discovery often then canonicalizes that formal system—but they are distinct operations. Canonicalization is about authority and institutionalization; emergence is about discovery. The distinction matters because a formal system can emerge and be widely used without being canonical (people adopt it informally without institutional decree), and a canonical system can be imposed top-down without having emerged from practice (though such systems often fail to gain traction because they lack grounding in actual usage).

Finally, Emergent Formalization is distinct from Specification, though specifications can be formal and can emerge. Specification is the process of defining requirements, constraints, or detailed behavior of a system or artefact: a software specification details what the code should do, an engineering specification defines material properties and tolerances. Specification is about defining requirements and acceptance criteria. Emergent Formalization is about discovering and articulating the underlying logic and structure of a domain. They can coexist—a software specification often formalizes emergent patterns from prior code and usage—but they address different questions. Specification asks "what should this system do?" and is forward-looking (it guides creation). Emergent Formalization asks "what logic and structure does this activity or domain actually embody?" and is retrospective (it articulates what exists). A specification might be formal and precise; an emergent formalization might also be formal and precise; but one is prescriptive, the other is descriptive. The distinction matters because confusing them leads to over-specification (writing requirements that constrain beyond what is essential, locking in arbitrary choices) or under-specification (failing to capture essential patterns that users rely on). Emergent formalizations often inform specifications, translating tacit practice into explicit requirements.

Solution Archetypes

Solution archetypes in the catalog that build on this prime — directly (this prime is a source ingredient) or as a related prime.

Built directly on this prime (5)

• Collective Learning System: Capture local learning and propagate it across the system so adaptation does not remain isolated.
  ▸ Mechanisms (8)
• Emergent Formalization: Convert repeated informal practice into explicit standards, roles, protocols, or institutions once the pattern has stabilized.
  ▸ Mechanisms (11)
• Emergent Role Formation: Allow roles to emerge from observed contribution patterns before formalizing or supporting them.
  ▸ Mechanisms (10)
• Proceduralization: Convert tacit or inconsistent work into explicit repeatable steps with inputs, outputs, and exception handling.
  ▸ Mechanisms (10)
• Symbolic Convention Governance: Create, document, maintain, and revise arbitrary symbolic conventions so shared meaning remains stable enough for coordination.
  ▸ Mechanisms (9)

Also a related prime in 3 archetypes

• Informal Structure Mapping: Reveal the unofficial relationships, workarounds, and influence paths that determine how work actually gets done.
• Organization–Artifact Topology Alignment: When the structure of a produced artifact is likely to mirror the collective that built it, map both topologies and redesign either the artifact boundaries, the team boundaries, or the communication paths instead of letting the mirror form accidentally.
• Semantic Drift Monitoring: Monitor how meanings change over time so terminology, policy, symbols, and shared understanding stay aligned before silent misunderstanding accumulates.

Notes

Linguistic-pragmatics origin (Bühler's Sprachtheorie 1934 introduced the "origo" of speaker/here/now; Fillmore 1971/1997; Levinson 1983). Software-systems transfer is well-established in template engines, internationalization frameworks, and log-schema design. Companion to #322 contextual_mode_switching (which concerns switching whole communicative modes based on context, while deixis operates on individual referential expressions within any mode). Companion to #320 cooperative_principle_gricean_maxims (which governs how hearers infer speaker meaning, including deictic resolution). Companion to #315 speech_act_theory_illocution_perlocution (which describes the pragmatic force of utterances; deixis specifies how context is bound into those utterances' reference).

References

[1] Bybee, Joan L. Language, Usage and Cognition. Cambridge University Press, 2010. Usage-based grammar: chunking of high-frequency sequences, token-frequency effects, phonetic reduction and reanalysis driving grammaticalization — supports the frequency-driven chunking and going-to/gonna mechanism claims. ↩

[2] Hopper, Paul J., & Traugott, Elizabeth Closs. Grammaticalization (2^nd ed.). Cambridge University Press, 2003. The unidirectional cline (lexical to grammatical) with semantic bleaching and decategorialization — supports the cline, unidirectionality, and going-to/gonna trajectory claims. ↩

[3] Bybee, Joan; Perkins, Revere; & Pagliuca, William. The Evolution of Grammar: Tense, Aspect, and Modality in the Languages of the World. University of Chicago Press, 1994. Cross-linguistic survey (76 languages) showing token-frequency-driven, unidirectional lexical-to-grammatical change — supports the frequency-effect-mechanism and one-way-process claims. ↩

[4] Hopper, Paul J. "On Some Principles of Grammaticization". In E. C. Traugott & B. Heine (Eds.), Approaches to Grammaticalization, Vol. I, pp. 17–35. John Benjamins, 1991. States principles (layering, divergence, specialization, persistence, decategorialization) distinguishing grammaticalization from mere conventionalization — supports the 'grammaticalization produces rule-governed morphosyntactic units' claim. ↩

[5] Haspelmath, Martin. "On Directionality in Language Change with Particular Reference to Grammaticalization". In O. Fischer, M. Norde & H. Perridon (Eds.), Up and Down the Cline: The Nature of Grammaticalization, pp. 17–44. John Benjamins, 2004. Examines alleged de-grammaticalization counterexamples to strict unidirectionality (accepting only a few) — supports the 'Haspelmath challenges strict unidirectionality, citing counterexamples' claim. ↩

[6] Heine, Bernd, & Kuteva, Tania. World Lexicon of Grammaticalization. Cambridge University Press, 2002. A-Z typological lexicon documenting the cross-linguistic source-to-target grammaticalization pathways — supports the 'cross-linguistically supported pathways' claim. ↩

[7] Traugott, Elizabeth Closs, & Dasher, Richard B. Regularity in Semantic Change. Cambridge University Press, 2002. Shows semantic-change types follow predictable, largely unidirectional pathways recurring across unrelated languages — supports the 'same semantic pathways repeat across languages' claim (and is reused for the emoji/formalization example). ↩

[8] Bybee, Joan. "Mechanisms of Change in Grammaticization: The Role of Frequency". In B. Joseph & R. Janda (Eds.), The Handbook of Historical Linguistics, pp. 602–623. Blackwell, 2003. Argues high-frequency tokens drive reduction and reanalysis, paralleling acquisition patterns — supports the language-acquisition / frequency-reduction claim. ↩

[9] Croft, William. Explaining Language Change: An Evolutionary Approach. Longman, 2000. Evolutionary/usage-based model distinguishing innovation, propagation, and fixation of changes through speech communities — supports the computational-modeling / propagation claim about how innovations spread. ↩

[10] Kuteva, Tania. Auxiliation: An Enquiry into the Nature of Grammaticalization. Oxford University Press, 2001. Detailed study of verb-to-auxiliary grammaticalization (auxiliation) as a subfield with its own chains and mechanisms — supports the grammaticalization-vs-lexicalization boundary discussion in T2. ↩

[11] Traugott, Elizabeth Closs. "Constructions in Grammaticalization". In B. Joseph & R. Janda (Eds.), The Handbook of Historical Linguistics, pp. 624–647. Blackwell, 2003. Treats grammaticalization as construction change driven by semantic specialization and functional need — supports the cognitive-vs-functional-motivation (Hopper functional side) discussion in T3. ↩

[12] Lehmann, Christian. Thoughts on Grammaticalization (3^rd ed.). Language Science Press, 2015. The classic parameters/criteria of grammaticalization (attrition, paradigmaticization, obligatorification, etc.) supporting strong unidirectionality with caution on universals — supports the cross-linguistic-universals-vs-variation claim in T4. ↩

[13] Cresswell, M. J. (1973). Logics and Languages. Methuen. Cresswell Logics and Languages modal logic indexical expressions.

[14] Anderson, J. A. (2017). Computational Reflection in the ML Family. In ACM Computing Surveys, 50(1), 1–37. Anderson computational reflection survey meta-programming reflection APIs scalability.